Question 1208844: Mike works at a grocery store and delivers newspapers. He earns $7 per hour at the grocery store and $10 per hour delivering newspapers. He can work no more than 20 hours per week. Graph two inequalities that Mike can use to determine how many hours he needs to work at each job to earn at least $90.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of hours worked at the grocery store
y = number of hours delivering newspapers
The two inequalities Mike would graph are
The first inequality is the constraint where Mike is able to work at most 20 hours, i.e. 20 hours or fewer.
The other inequality is making his total earnings (7x+10y dollars) to be $90 or larger.
7x = amount earned just from the grocery store
10y = amount earned from delivering newspapers
The line x+y = 20 goes through (0,20) and (20,0).
We shade below this line to graph  . This boundary line is solid because of the "or equal to".
The line 7x+10y = 90 goes through (0,9) and (10,2). We shade below above line to graph  . This boundary is also solid.
These two regions overlap to help form the solution set.
This is denoted as region R shown below.
x+y = 20 is the green line
7x+10y = 90 is the blue line
We focus only on the upper right quadrant where  and  since it makes no sense to have x or y be negative.
Region R is a quadrilateral with these vertex points
(0,9), (0,20), (20,0), (12.8571, 0)
The decimal value is approximate.
A few selected points in region R would be:
(2, 13), (5, 10), and (9, 9)
I'll let the student verify each point with the constraint inequalities.
A point like (4,16) is on a solid boundary line, which means we include it as part of the solution set.
A point like (5,22) is not inside region R, and not on the boundary either, so it's not a solution point.
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